STAT 410
Spring 2008
Homework #5
(due Friday, February 22, by 3:00 p.m.)
1.
Let X, Y, and Z be i.i.d. Uniform
[
0
, 1
] random variables Find the probability
distribution of W = X + Y + Z. That is, find
( )
w
f
W
.
Hint
:
If V = X + Y, we know the
p.d.f. of
V,
f
V
(
v
)
(
see Examples for 02/11/2008
):
f
V
(
v
) =
v
if 0 <
v
< 1,
f
V
(
v
) = 2 –
v
if 1 <
v
< 2,
f
V
(
v
) = 0
otherwise.
Now use convolution formula to find the
p.d.f. of W = V + Z.
There will be 5 possible cases, 2 of them are "boring".
2.
Suppose the size of largemouth bass in a particular lake is uniformly distributed
over the interval 0 to 8 pounds. A fisherman catches (a random sample of) 5 fish.
a)
What is the probability that the smallest fish weighs less than 2 pounds?
b)
What is the probability that the largest fish weighs over 7 pounds?
c)
What is the probability that the largest fish weighs between 6 and 7 pounds?
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 Spring '08
 Monrad
 Probability, Probability theory, Discrete probability distribution, independent random variables, joint PDF

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